Evaluate -5/6e-2/3e=-24

$- \frac{5}{6} e - \frac{2}{3} e = - 24$

Step 1

Simplify each term.

Combine $e$ and $\frac{5}{6}$ .

$- \frac{e \cdot 5}{6} - \frac{2}{3} \cdot e = - 24$

Move $5$ to the left of $e$ .

$- \frac{5 \cdot e}{6} - \frac{2}{3} \cdot e = - 24$

Combine $e$ and $\frac{2}{3}$ .

$- \frac{5 e}{6} - \frac{e \cdot 2}{3} = - 24$

Move $2$ to the left of $e$ .

$- \frac{5 e}{6} - \frac{2 e}{3} = - 24$

Step 2

To write $- \frac{2 e}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 e}{6} - \frac{2 e}{3} \cdot \frac{2}{2} = - 24$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 e}{3}$ by $\frac{2}{2}$ .

$- \frac{5 e}{6} - \frac{2 e \cdot 2}{3 \cdot 2} = - 24$

Multiply $3$ by $2$ .

$- \frac{5 e}{6} - \frac{2 e \cdot 2}{6} = - 24$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 e - 2 e \cdot 2}{6} = - 24$

Step 5

Simplify the numerator.

Multiply $2$ by $- 2$ .

$\frac{- 5 e - 4 e}{6} = - 24$

Subtract $4 e$ from $- 5 e$ .

$\frac{- 9 e}{6} = - 24$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 9$ and $6$ .

Factor $3$ out of $- 9 e$ .

$\frac{3 (- 3 e)}{6} = - 24$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 (- 3 e)}{3 (2)} = - 24$

Cancel the common factor.

$\frac{3 (- 3 e)}{3 \cdot 2} = - 24$

Rewrite the expression.

$\frac{- 3 e}{2} = - 24$

Move the negative in front of the fraction.

$- \frac{3 e}{2} = - 24$